18 research outputs found
Stochastic flow simulation and particle transport in a 2D layer of random porous medium
A stochastic numerical method is developed for simulation of flows and particle transport in a 2D layer of porous medium. The hydraulic conductivity is assumed to be a random field of a given statistical structure, the flow is modeled in the layer with prescribed boundary conditions. Numerical experiments are carried out by solving the Darcy equation for each sample of the hydraulic conductivity by a direct solver for sparse matrices, and tracking Lagrangian trajectories in the simulated flow. We present and analyze different Eulerian and Lagrangian statistical characteristics of the flow such as transverse and longitudinal velocity correlation functions, longitudinal dispersion coefficient, and the mean displacement of Lagrangian trajectories. We discuss the effect of long-range correlations of the longitudinal velocities which we have found in our numerical simulations. The related anomalous diffusion is also analyzed.researc
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Stochastic analysis of an elastic 3D half-space respond to random boundary displacements : exact results and Karhunen-Loéve expansion
A stochastic response of an elastic 3D half-space to random
displacement excitations on the boundary plane is studied. We derive exact
results for the case of white noise excitations which are then used to give
convolution representations for the case of general finite correlation length
fluctuations of displacements prescribed on the boundary. Solutions to this
elasticity problem are random fields which appear to be horizontally
homogeneous but inhomogeneous in the vertical direction. This enables us to
construct explicitly the Karhunen-Loève (K-L) series expansion by solving
the eigen-value problem for the correlation operator. Simulation results are
presented and compared with the exact representations derived for the
displacement correlation tensor. This paper is a complete 3D generalization
of the 2D case study we presented in J. Stat. Physics, v.132 (2008), N6,
1071-1095
Analysis of relative dispersion of two particles by Lagrangian stochastic models and DNS methods
Comparisons of the Q1D against the known Lagrangian stochastic well-mixed quadratic form models and the moments approximation models are presented. In the case of modestly large Reynolds numbers turbulence (Re λ ⋍ 240) the comparison of the Q1D model with the DNS data is made. Being in a qualitatively agreemnet with the DNS data, the Q1D model predicts higher rate of separation. Realizability of Q1D model extracted from the transport equation with a quadratic form of the conditional acceleration is shown
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Elastostatics of a half-plane under random boundary excitations
A stochastic analysis of an elastostatics problem for a half-plane
under random white noise excitations of the displacement vector prescribed on
the boundary is given. Solutions of the problem are inhomogeneous random
fields homogeneous in the longitudinal direction. This is used to model the
displacements and represent their correlation tensor via spectral expansion.
This approach makes it possible to derive exact representations for other
functionals of interest, in particular, the vorticity, the strain tensor, and
the elastic energy